As seen in Fig. REF b, the effective operator \(\mathcal {O}_7\)  can be induced by the one-loop diagram, whereas the Weinberg operator cannotThere is a similar realization of \(\mathcal {O}_7\)  in Ref. [1]}, in which a triplet replaced the singlet \(s\)  of our model. A fundamental distinction of their paper from the present one is that \({\cal O}_7\)  does not give the dominant contribution to Majorana neutrino masses in Ref. [1]}..
Consequently, Majorana neutrino masses appear through the two-loop diagram in Fig. REF cSimilar topology with one \(W^\pm \)  exchange in a two-loop neutrino mass model can also be found in Refs. [3]}, [4]}, in which a different high-dimensional effective operator is realized without DM.. The resulting neutrino mass matrix \(M_\nu \)  defined in the Lagrangian \(-{1\over 2}\overline{(\nu _L^c)}_l (M_\nu )_{ll^{\prime }}(\nu _L)_{l^{\prime }}+{\rm H.c.}\) 
can be calculated as
\((M_\nu )_{ll^{\prime }}=-{1\over (16\pi ^2)^2}{G_F s_{2\theta }\over \sqrt{2}}(M_{H}^2-M_{A}^2)\sum _{i=1,2,3}(m_l\,\zeta _{il}\,\xi _{il^{\prime }}+m_{l^{\prime }}\,\zeta _{il^{\prime }}\,\xi _{il})[I_{i1}-I_{i2}]\;,\) 
